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Article Dans Une Revue Linear Algebra and its Applications Année : 2019

Inequalities for the eigenvectors associated to extremal eigenvalues in rank one perturbations of symmetric matrices

Résumé

This paper considers the eigenvectors involved in rank one perturbations of symmetric matrices. A doubly stochastic matrix based on the inner products between initial and perturbed eigenvectors is introduced to derive several relations for the latter ones. A majorization theorem used together with this doubly stochastic matrix provides the main results of the paper, which deal with the eigenvectors associated to the largest and smallest non-zero eigenval-ues. Further developments are also suggested for infinitesimal perturbations using convergent power expansions of both eigenvalues and eigenvectors. *
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Dates et versions

hal-01902562 , version 1 (23-10-2018)

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Jacques Bénasséni, Alain Mom. Inequalities for the eigenvectors associated to extremal eigenvalues in rank one perturbations of symmetric matrices. Linear Algebra and its Applications, 2019, 570, pp.123-137. ⟨10.1016/j.laa.2019.01.021⟩. ⟨hal-01902562⟩
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